Journal of Hydro-Environment Research 1 (2007) 1e11www.elsevier.com/locate/jher

Digital Yellow River Model

Guangqian Wang, Baosheng Wu*, Tiejian Li

State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, China

Received 11 February 2007; revised 15 March 2007; accepted 23 March 2007

Abstract

Soil erosion is one of the key concerns in land use management for the Loess Plateau of the Yellow River, where serious soil loss is the rootcause of environmental and ecological degradation of the basin. In this paper, a physically-based, distributed-parameter, and continuous erosionprediction model at the river basin scale was developed with the aim of assisting in developing better land use management strategies. Theframework, the major supporting techniques, and the typical erosion processes are described. The physical processes of sediment yield and trans-port in the Loess Plateau are divided into three sub-processes, including the runoff and sediment yield on hillslopes, gravitational erosion ingullies, and hyperconcentrated flow routing in channels. For each sub-process, a physically-based simulation model was developed and embed-ded into the whole model system. The model system was applied to simulate the runoff and sediment yield in several typical years in the coarsesediment source area of the Loess Plateau, and the simulated results were in reasonably good agreement with the measured values.� 2007 International Association for Hydraulic Engineering and Research, Asia Pacific Division. Published by Elsevier B.V. All rights reserved.

Keywords: Yellow River; Loess Plateau; Erosion model; Sediment yield; Soil and water conservation

1. Introduction

The Yellow River is notorious because of its high sedimentload, which originates at the Loess Plateau, located at the mid-dle reaches of the river. Serious soil erosion occurs frequentlyfollowing storm events in the summertime, with the conse-quence of severe soil loss and degradation of the environmentin the upland area, as well as channel aggradation at the lowerreaches of the river. Soil and water conservation in the LoessPlateau is of critical importance to the integrated basin man-agement of the river. For this reason, an integrated soil erosionmodel is highly desirable, in order to help develop better landuse management strategies.

To simulate the spatial and temporal distribution of the sed-iment yield at any point and time, a complex system of inter-acting processes has to be simulated, including rainfall events,vegetation growth, surface runoff, subsurface and ground flow,soil detachment, transport and deposition. Excellent examples

* Corresponding author.

E-mail address: baosheng@tsinghua.edu.cn (B. Wu).

1570-6443/$ - see front matter � 2007 International Association for Hydraulic Enginee

doi:10.1016/j.jher.2007.03.001

of physically-based simulation systems that integrate a widerange of interacting processes important for land use manage-ment are WEPP (Water Erosion Prediction Project) (Flanaganand Nearing, 1995; Laflen et al., 1997), ANSWERS (AreasNon-point Source Watershed Environmental Response Simu-lation) (Beasley et al., 1980), LISEM (Limburg Soil ErosionModel) (Jetten, 2002), and EUROSEM (European Soil Ero-sion Model) (Morgan et al., 1998a,b). In these physically-based, distributed erosion models, an area is divided intosub-units, each having uniform characteristics of slope, soiland land cover. These sub-units are then arranged in sequenceto form a cascade through which water and sediment move-ment can be routed from the top to the bottom of the hillsidesand from upstream to downstream along the river channels.

For widely used distributed erosion models, such as WEPP,ANSWERS, LISEM, and EUROSEM, each has limitations interms of its representation of erosion processes if it is to be ap-plied to the Loess Plateau of the Yellow River. First, the sed-iment concentration in this region can easily reach 1000 kg/m3

due to the highly erodible ground surface, which rarely hap-pens in other river basins. Second, the hillslopes are so steep

ring and Research, Asia Pacific Division. Published by Elsevier B.V. All rights reserved.

2 G. Wang et al. / Journal of Hydro-Environment Research 1 (2007) 1e11

that they exceed the assumption of gentle slope in most ero-sion models. Third, gravitational erosion happens frequentlyin the area between the hillslopes and the channel, but this pro-cess rarely occurs in other river basins and therefore it is notconsidered in most soil erosion models.

Soil erosion modeling of the Loess Plateau has been widelydiscussed and great efforts have been made by many scientistsin China to create a soil erosion model to represent the uniquecharacteristics of the Loess Plateau. Some of the physically-based models for the process of rainfall-runoff-soil erosionare those developed by Tang et al. (1990), Tang and Chen(1994), and Cai et al. (1996). In these models, each basinunit is divided into several geomorphic units from the top tothe bottom of the hillsides based on the topographical and geo-morphic conditions. Then for each geomorphic unit, a differenterosion module is used according to the physical processes.Beginning in 2000, a team of researchers at Tsinghua Univer-sity took the initiative and developed a physically-based, dis-tributed-parameter and continuous erosion prediction modelat the river basin scale that can best represent the erosion pro-cesses of the Loess Plateau. This soil erosion model wasnamed the Digital Yellow River Model (DYRIM) because ittook the advantage of digital terrain data, drainage networkcodification, RS- and GIS-based parameter acquisition, andparallel computation to support the realization and operationof the model layer. This paper is a summary and introductionof the framework, key features and formulations of theDYRIM erosion model.

2. Framework of the DYRIM

The architecture of the DYRIM is shown in Fig. 1. Thereare four layers in the model, namely, the data layer, modellayer, application layer, and post processing layer. The data

layer, which is the basis of the model, provides the functional-ity to store and process basic data obtained from differentsources, such as digital terrain data, remote sensing images,and field measurements. Different types of data can be trans-formed or interpreted by GIS-based data processing to bestored in a thematic database, which is accessed by the modellayer and application layer. The data layer also provides themodel with the ability to acquire and modify various typesof parameters that are necessary for the computation of differ-ent physical processes. In addition, the database enables datato be shared and exchanged very efficiently, which facilitatesthe implementation of large river basin scale modeling.

The model layer is the kernel of the DYRIM, where inte-grated simulation of the soil erosion process takes place.This layer is represented as program modules to calculatethe sub-processes of soil erosion and sediment transport.These modules are managed as a model library, which has a de-fined interface, enabling the adoption of more modules. In thisway, the model layer will become more powerful as furtherimproved models for the physical processes are added to thesystem following relevant academic advances.

The application layer deals with various needs in land useand river engineering to support better management strategies.The evaluation of soil conservation practices, flood warning,geo disaster prevention, and river sedimentation managementare realized in this layer. Further analysis and utilization ofthe simulated results are done in the post processing layer.

Overall, the soil erosion process models are the core of thesystem, and all of the other components are supporting tech-niques to assist the running of these simulation models. Thesesupporting techniques also include the solving of some addi-tional issues that are encountered in intra-layers or inter-layerswhen organizing the architecture of the model, such as dataschema, river basin decomposition, etc. These issues need to

Hyd

rody

nam

ic M

odel

Thematic Database for the Digital Watershed Model

Mod

el L

ayer

Digital Terrain Data

Remote Sensing Data

Precipitation Data

GIS Based Data

Processing

Water-Soil Conservation

Scheduling

Water and Sediment

Reduction Analysis

Disaster Prewarning

Application Layer

Data Layer

Underlying Data

Water Yield Model

Sediment Yield

Model

For Hillslopes:

……Post Processing

Data Mining and

Analysis

GIS & VR Based

Data Visualization

……

Affluxion Model

For Channels:

……

Gravity Erosion

Model

Fig. 1. The framework of the Digital Yellow River Model.

3G. Wang et al. / Journal of Hydro-Environment Research 1 (2007) 1e11

be resolved in order to elevate the efficiency and capacity ofthe model.

3. Supporting techniques of the DYRIM

The important supporting techniques of the DYRIM in-clude the database, GIS, remote sensing, virtual reality andparallel computation. Among them, the digital elevation model(DEM), drainage network codification and partitioning, pa-rameter acquisition and parallel computing make the DYRIMdiffer from other fields of informatization.

3.1. Application of the DEM

As an important format of digital terrain data, the DEM isthe basis of the DYRIM. The geometrical parameters of sim-ulation models, such as channel density, gradient of hillslopes,length and gradient of channel segments, are all extracted fromthe DEM. The application of the DEM makes it possible toachieve distributed and physically-based hydrological models,and provides basic data for physically-based sediment yieldmodels. However, with the enlarged spatial scale, high resolu-tion DEM data must be partitioned in order to be stored andread. Liu et al. (2004) developed procedures to achieve thewhole process of acquisition, pre-processing, partitioned stor-age and reading.

There are two types of methods for the application of theDEM. One discretizes the equations for water and contami-nants directly on the DEM points in order to solve them; theother divides a watershed into elements according to topogra-phy, and applies integrated or generalized equations to solvethe issues under the assumption of uniform topography and pa-rameters in each unit. The DYRIM adopts the latter method,and takes hillslope-channel units to reflect the nature of a wa-tershed. Extraction of drainage networks is usually accom-plished by the D8 method (O’Callaghan and Mark, 1984)and its improvements. The DYRIM adopts the TOPAZ module(Garbrecht and Martz, 1999) based on this method.

3.2. Drainage network codification and partitioning

Discharge routing and sediment transport simulation shouldtake place on the hillslope-channel units following the orderfrom upstream to downstream. The well-known Horton-Strah-ler order basically reflects the affluxion order of drainage net-works. However, to make topological algorithms moreeffective, a new drainage network codification method is pro-posed in the DYRIM (Li et al., 2006b). In this method, a den-tritic river is considered as a binary tree, and each channelsegment is assigned two numbers in terms of (BSLength,BSValue). The BSLength is the level number of the segmentin the binary tree, and represents the logical distance to theoutlet of the watershed. The BSValue is the sequence numberof the segment in its level of the binary tree, and represents thelogical distance to the mainstream of the drainage network.Thus, the topology of a drainage network can be expressed

by the river codes, and river segments can be retrievedeffectively.

To make the codification method applicable to large re-gions, a policy of grading and sub-zoning following the patternof a river’s tributaries is adopted. The codification method isused in each tributary separately, and each tributary has itsown grade and position number. The grade number is equalto its tributary grade and the position number increases from0 near the outlet to upstream one by one.

3.3. Parameter acquisition

The parameters of the DYRIM are spatially distributed. Thegeometrical parameters are acquired from the DEM, as men-tioned before, and the underlying surface parameters are ac-quired from remote sensing images in the format of rasterdata. These underlying parameters include vegetation cover,land use, soil type, potential evaporation, etc. To make the ras-ter data match the hillslope-channel units, the central point orpolygon border of each hillslope-channel unit is used to cap-ture the point values of the raster data (Chen et al., 2005).The values are then counted and transformed into correspond-ing parameters. This process fits all kinds of distributed pa-rameter acquisition.

Parameters acquired from both the DEM and the raster dataare all stored in a thematic database to be accessed by simula-tion models. Each record in the parameter table representsa channel segment and its corresponding hillslopes, as shownin Table 1. The mapping relationship of the records and thedrainage network is shown in Fig. 2.

3.4. Cluster-based parallel computing

Simulation models constitute an enormous computationmission for the DYRIM. If a serial algorithm is adopted, thetime cost will be unacceptable, and the efficiency of the

Table 1

Acquired parameters from both DEM and raster data

Parameter Declaration Record 47 Record 46

StrahlerOrder Horton-Strahler order 1 2

BSValue Value number of the river code 2056 1028

BSLength Length number of the river code 16 15

AreaSource Area of the source hillslope 10,000 m2 �1

AreaRight Area of the right hillslope 11,250 m2 18,750 m2

AreaLeft Area of the left hillslope 6250 m2 8750 m2

SlopeSource Gradient of the source hillslope 0.0358 �1

SlopeRight Gradient of the right hillslope 0.0509 0.0569

SlopeLeft Gradient of the left hillslope 0.0355 0.037

Slope Riverbed gradient of channel

segment

0.0145 0.0044

Length Length of channel segment 170.5 m 191.5 m

MiddleX X coordinate of the central point 106.767 106.8729

MiddleY Y coordinate of the central point 35.2075 35.229

SoilType Soil type 2 2

LandUse Land use 6 6

LAI Leaf area index 1.20 1.20

.. .. .. ..

4 G. Wang et al. / Journal of Hydro-Environment Research 1 (2007) 1e11

database will not be maximized. With the development ofcluster technology, parallel computing has been applied inmany specialized fields. Among the parallel programming lan-guages, MPI (Message Passing Interface) (MPI Forum, 2006)is the most popular one. The DYRIM employs the MPI stan-dard because of its platform independence, plentiful functionsand high efficiency (Li et al., 2006a).

The units in the DYRIM have the significant characteristicof low correlation, which meets the conditions for parallelcomputing. The adopted parallel policy is the domain

1 21 1

4746

(16,2056)

(15,1028)

1

1

1

2

Right

Left

Source

Left

Right47

462

Fig. 2. Mapping relation of the channel segments in Table 1 (the numbers in

the parenthesis are the river code numbers of BSLength and BSValue).

decomposition of drainage networks. That is, the river is bro-ken into independent tributaries to enable synchronous simula-tion. To make the order of the calculation match the order offlow affluxion, river tributaries are generated dynamicallyfrom upstream to downstream. Thus, a master-slave modelwas adopted to organize cluster computing.

4. Formulation of natural processes

4.1. Mechanism of sediment yield and transport

Various phenomena and internal mechanisms are present inthe natural processes of sediment yield and transport in differ-ent reaches. In the middle reach of the Yellow River, the LoessPlateau is classified into several categories, such as gulliedrolling loess regions, gullied loess plateau regions, dune areas,earth and rock mountains and loess terrace regions. The gul-lied rolling loess and gullied loess plateau regions are thetwo regions that have much in common, and represent themost typical processes and mechanisms of flow and sedimenttransport in the coarse sediment source area of the LoessPlateau. The coarse sediment source area is located fromthe Huangfuchuan River in the north down to the WudingRiver in the south (Fig. 3), and covers an area of about78,600 km2. Floods from this region are responsible for mostof the coarse sediment deposited in the lower Yellow River(Qian et al., 1980). Because of this, soil erosion issues andconservation management are mainly focused on this region.

The terrain in this area is fractured and complicated. How-ever, it can be divided into two parts, namely hillslopes andchannels. The upper part of the hillslope is flat upland. Wateroverflows from the top, gathers gradually as it travels down theslope and finally scours the soil to form tiny rills, which de-velop into shallow gullies downward. The shallow gulliesare almost connected with permanent gullies through verticaldrops. At the same time, permanent gullies are next to the

Fig. 3. Map of the Yellow River basin.

5G. Wang et al. / Journal of Hydro-Environment Research 1 (2007) 1e11

channel. The area between a hillslope and channel is referredto as a gully area. Gully areas are steep and fractured.

The channels are transport passages for water and sediment,where scouring and deposition also occur frequently. Accord-ing to their sizes, the channels of the coarse sediment sourcearea can be divided into four types: tiny channels, tributarychannels, main channels and river channels. In short, hillslopesand channels altogether compose the hillslope-channel system(Fig. 4), and the profile of the hillslope-channel unit is shownin Fig. 5.

Although different processes occur in different parts of thehillslope-channel system, they are interconnected as a whole,and compose various complex physical processes, such as ero-sion, transport, and deposition, and which finally bring sedi-ment to the exit of the watershed. All of the processes canbe categorized into three main sub processes: water and sedi-ment yield on hillslopes, gravitational erosion in gullies andhyperconcentrated flow routing in channels.

The hillslope erosion is abstracted into three phases: sputtererosion, sheet erosion and tiny and shallow gully erosion. Ac-cording to the experimental data based on typical surface flowfield research, the quantity of sediment erosion that forms thetiny and shallow gullies accounts for 36% of the total, and the

Fig. 4. Typical hillslope-channel system on the Loess Plateau (Zhang, 1993).

sputterregion

sheetwashregion

tiny & shallow gully region

permanent gully region

channel

Fig. 5. Different regions of hillslope-channel system on the Loess Plateau.

maximum sediment concentration of gully erosion exceedsthat of sputter erosion by 30% (Wang et al., 1982). However,the total quantity of the detached soil increases along the hill-slope, and can be generalized as a single erosion processaffected by hydrodynamic forces.

Based on the analysis of a large amount of measured data,there exists a phenomenon that the sediment discharge peaklags behind the flood peak on the Loess Plateau. When thisphenomenon becomes most notable, it is usually associatedwith the occurrence of gravitational erosion. There are manykinds of gravitational erosion, among which landslides andcollapses are the most dominant. The steep slope and the char-acteristics of loess soil are the main dynamical factors leadingto gravitational erosion, while rainfall and runoff also playa major role in inducing the occurrence of gravitational ero-sion. Among all the main factors, the nature of the soil and mi-cro-landscape are random, which ultimately makesgravitational erosion a stochastic process, which can be trig-gered by specific factors.

In drainage networks, hillslope runoff and detachment ofgravitational erosion are superposed from upstream to down-stream. Therefore, the flow discharge and sediment concentra-tion increase, which finally leads to a hyperconcentrated flow.Hyperconcentrated flows in channels have some special prop-erties: (1) Because of the lag of gravitational erosion and in-creased sediment transport capacity of hyperconcentratedflows, the sediment discharge peak usually lags behind theflood peak, and lasts longer. With the increasing order of chan-nels, this phenomenon will become more obvious; (2) Due tothe randomness of gravitational erosion and scouring and de-position in channels, the relationship between discharge andsediment concentration becomes unclear; (3) In a single flood,scouring and deposition in channels and gradation adjustmentmake particles small at low sediment concentrations andcoarse at high sediment concentrations, and the difference in-creases with the channel’s order increasing. Therefore, in or-der to describe the nature of hyperconcentrated flows,channels should be treated as a separate and important partof the whole. Major factors such as the confluence area, riverbed gradient, cross-section profile of channels and gravita-tional erosion quantity must all be taken into account to sim-ulate the natural processes in drainage networks.

4.2. Model of runoff and sediment yield on hillslopes

Many researchers have proven that, of many channel for-mulae, the Yalin equation is the most practicable to computesediment transport for hillslope flows, and it has been incorpo-rated into several integrated models (Ahmadi et al., 2006).However, the Yalin equation may not be suitable for the LoessPlateau because of the possible underestimation of the sedi-ment yield.

In this paper, a conceptual hillslope runoff yield model isproposed, which considers mainly Horton flow and calculatesinfiltration based on the theory of soil hydrodynamics to sim-ulate continuous hillslope surface runoff. Based on the simu-lated surface runoff, the sediment yield calculation unifies

6 G. Wang et al. / Journal of Hydro-Environment Research 1 (2007) 1e11

sputter erosion, sheet erosion and shallow gully erosion toa generalized process whose detachment quantity increaseswith the reinforced surface flow along the hillslope (Wanget al., 2005a).

Assume that the thickness of the detached soil increasesalong the hillslope, with the increasing rate of m layers perunit length as shown in Fig. 6. The average velocity of thesediment movement (vs) is slower than that of the water flow(v), and v can be calculated by Manning’s equation, so:

vs ¼ av¼ aq25n�

35J

310; ð1Þ

where a is the delayed ratio of sediment from the water flow,less than 1; q is the discharge per unit width from the runoffyield calculation; n is the Manning’s roughness coefficient;and J is the surface slope.

Sediment yield per unit time per unit area (e) can be ex-pressed by vs as:

e¼ p

6mDrsvs ¼

p

6mDrsaq

25n�

35J

310; ð2Þ

where D is the diameter and rs is the density of the sedimentparticles.

Assuming that soil erosion is distributed uniformly in thecontour direction of the slope, the total amount of erosion forthe whole hillslope in unit time interval (E ) can be obtainedby integrating Eq. (2) along the downslope direction and mul-tiplying by the hillslope width. The flat shape of the hillslope isexpressed by its area A and downslope length L, so:

E¼ 5ap

42mDrsA

35Q

25n�

35J

310L

25; ð3Þ

where Q is the total flow discharge at the foot of the hillslope(m3/s).

The value of m is relevant to the erosion agent of flow andthe erosion resistance characteristics of the surface soil, and itcan be expressed as:

m¼ ktb0 ¼ k

�gb

mq35 bn

35 bJ

710 b�; ð4Þ

νs

m

Detached soil

Observation

section

Steady soil

Fig. 6. Generalized scheme of hillslope erosion.

where k and b are the coefficients related to land use and theerosion resistance characteristics of the soil, they will be cali-brated before calculation, and b< 1; t0 is the shear stress ofthe turbid flow; and gm is the specific weight of the turbidflow. Putting Eq. (4) into Eq. (3), the final expression of thesediment yield on the hillslope surface is obtained:

E¼ 5

42apAkr bþ1

s g bq35 bn

35 b�3

5L25D

�Q

A

�25

J7

10 bþ 310: ð5Þ

4.3. Gravitational erosion in gully areas

Gravitational erosion is calculated according to stabilityanalysis based riverbank erosion (Osman and Thorne, 1988;Darby and Thorne, 1996). However, the characteristics of un-saturated loess and the induction effect of slope surface floware specialized in this paper to identify gravitational erosion.The simulation is established in the gully region, and considersthe collapse or sliding of the soil body as the subject, and in-cludes the analysis of the mechanical condition of the soilbody (Wang et al., 2005b).

As shown in Fig. 7, the forces on the soil body include: (1)gravity (Wt), and the increment caused by water soaking isconsidered; (2) anti-slide force (FR) on the slide-crack surface,and the reduction of cohesive strength caused by the incrementof soil moisture is considered; (3) water pressure (T ) in thetension crack along the loess vertical cleavage at the top ofthe soil body.

To calculate the forces above, the infiltration can be ob-tained by the runoff yield simulation model of the system.

Flow inchannel

Lateralerosion

Hydro-compaction

Watersoaking Increasing

Wt

RainfallRunoff

Decreasing FR

FD

T

Fig. 7. The forces on the sliding soil body.

7G. Wang et al. / Journal of Hydro-Environment Research 1 (2007) 1e11

The shear strength of the unsaturated soil (Sr) can be expressedapproximately by:

Sr ¼ cþ s tan f¼ c0 þ t0 þ s tan f; ð6Þ

where c is the nominal total cohesive strength; c’ correspondsto the cohesive strength of the saturated soil; t’ is the addi-tional cohesive strength; s is the normal stress; and f is theinternal friction angle, which is assumed to be invariant withwater content.

According to the results reported by Dang and Li (1996),the additional cohesive strength is caused by capillary force,and has a power function with water content:

t0 ¼ awb; ð7Þ

where w is the water content (%); and a and b are coefficientsthat can be obtained through experiments.

Lateral erosion at the toe of the hillslope caused by the flowcurrent in channels can be simulated by the Osman (Osmanand Thorne, 1988) model. The fallback distance in the lateraldirection for the unit time interval (DB) can be calculated by:

DB¼ Cl� ðt� tcÞ � e�1:3tc

gs

; ð8Þ

where Cl is a coefficient that is related to the physicochemicalproperty of soil. According to experimental results, Cl can be3.6� 10�4. t is the shear stress of the water flow (Pa). tc is theincipient shear stress (Pa).

After that, the sliding force and sliding resistance can beexpressed as follows using known values of soil stress andgeometry:

FD ¼Wt sin qþ T cos q ð9Þ

FR ¼ Lf þWt cos q tan f; ð10Þ

where FD is the sliding force; q is the angle of the sliding face;FR is the sliding resistance; and Lf is the length of the failureplane.

Soil stress and geometry are time-variant with water con-tent. Therefore, at different time steps, different assurance co-efficients Fs¼ FR/FD will be obtained. However, to meet therandomicity of gravitational erosion, fuzzy analysis is appliedto the assurance coefficient, and finally the membership gradeof destabilization is achieved. Whether a random event hap-pens or not is judged when the model is running.

When failure is predicted to occur, the volume of failureblock per unit reach length can be calculated from geometry.Assume that the probability of failure along the channel reachis Pg; then the sediment yield caused by the gravitational ero-sion of each channel segment can be calculated. The detachedsediment is then added into the equation for sediment transportin the channel as lateral input, which makes the sediment con-centration increase to the sediment transport capacity. The lat-eral inputs last for several time steps until the gravitationaldetached sediment is used up.

4.4. Hyperconcentrated flow routing in channels

As the channels in the coarse sediment source area have nomeasured cross-section profile, but only basic parameters suchas the length and bed slope, the discharge routing model isbased on the diffusive wave method, and the channel cross-section is assumed to be V-shaped to obtain flow parameterssuch as stage and velocity to calculate the sediment transport.

Fig. 8. The linkage from the drainage network to a hillslope-channel unit.

8 G. Wang et al. / Journal of Hydro-Environment Research 1 (2007) 1e11

Fig. 9. Measured and simulated sediment concentrations in 1967: (a) Xizhuang station; (b) Caoping station.

The coefficients of the diffusive wave equation are calcu-lated with the four-point scheme:

hCi ¼X

Ci=4; hBi ¼ f ðhQi; hCiÞ; hQ=Ci

¼XðQi=CiÞ=4; i¼ 1;2;3;4; ð11Þ

where hi stands for the value of the calculation point, hCi isused to calculate the Muskingum K coefficient, and hBi andhQ=Ci are used to calculate the Muskingum x coefficient.

It was pointed out by Cappelaere (1997) that, if the hydrau-lic slope is approximated to be the bed slope, the differencebetween the diffusive wave method and the kinematic wavemethod can be ignored. Thus, the hydraulic slope (S ) is as-sumed to be:

S¼ S0þ hvh

vx; ð12Þ

where S0 is the bed slope; h is a coefficient that can be ex-pressed by:

h¼�

0:7� 1:0 for the rising limb0 for the receding limb:

ð13Þ

By using the h-form diffusive wave equation, vh=vx isconverted to the expression of known value Q

vh

vx¼ 1

BCh

vQ

vx; ð14Þ

where Ch ¼ ð1=BÞðvQ=vhÞ is the wave velocity coefficient ofthe h-form diffusive wave equation.

To prevent negative reactions, the space step should be lim-ited as:

Dx˛�

CDt� Q

BSC;CDtþ Q

BSC

�: ð15Þ

Therefore, with a defined time space, the channel withlength Lc is divided into several segments as:

N ¼ Int

�Lc

C,Dt

�; N � 1; ð16Þ

where C is the wave velocity coefficient, and Int() stands forthe operation of rounding.

Sediment transport is considered as the suspended loadtransport. The integrated format of the non-equilibrium sedi-ment transport equation is used:

S¼ S� þ ðS0� S0�Þe�aqLc

us þ ðS0� � S�Þq

ausLc

�1� e

�aqLcus

�; ð17Þ

where S and S0 are the sediment concentrations, S� and S0� arethe sediment transport capacities of the outlet and inlet cross-sections, respectively; a is the coefficient of saturation recov-ery; and us is the settling velocity of sediment particles.

4.5. Integration based on digital drainage network

Calculation methods in antecedent sections are coupled inthe digital drainage network. The digital drainage network isthe representative form of a river basin in the DYRIM. For ex-ample, the coarse sediment source area of the Loess Plateau ispartitioned into 4 grades and 37 tributaries. There are 84,618units in total, and the average hillslope area is about0.37 km2. Each hillslope-channel unit can be located in thedrainage network, as shown in Fig. 8.

During simulation, water and sediment yield, gravitationalerosion and hyperconcentrated flow routing are calculated sep-arately for different hillslope-channel units. The runoff andsediment yield of each hillslope are directly superposed ondischarge in the corresponding channel segment, and gravita-tional detached sediment enters the channel in the way men-tioned before. In the drainage network, the simulation orderof the hillslope-channel units follows the order from upper

Table 2

Values of selected important parameters

Parameter Value

Permeability coefficient of soil 10�8 to 10�4 m/s

Porosity of soil 0.15 to 0.40

b in formula (5) 0.3

k in formula (5) 0.005 to 1.0

Internal friction angle of loess 18� to 30�

9G. Wang et al. / Journal of Hydro-Environment Research 1 (2007) 1e11

Fig. 10. Distributions of runoff depth and erosion modulus simulated for the coarse sediment source area in 1967.

to lower reach to accord with affluxion. Therefore, calcula-tions of different sediment yield and transport sub processesare integrated in this way.

5. Application of DYRIM

5.1. Application in Chabagou watershed

The Chabagou watershed is located in the gullied rolling lo-ess region with a catchment area of 205 km2 (Fig. 3), and it isdivided into 1995 units with an average hillslope area of0.04 km2. Some simulation parameters were obtained frommeasured data, and some others were calibrated by simulation

of the year 1961. Selected results for the flood season of 1967are shown in Fig. 9.

1967 was a year of high sediment yield in Chabagou water-shed. In this year, storm rainfall happened frequently, and in-duced hyperconcentrated flows several times. The simulationresults reflected the sediment yield events with acceptableprecision.

5.2. Application in the coarse sediment source area

The highest annual sediment yield in the recorded historyof the Loess Plateau occurred in 1967 in the coarse sedimentsource area (Fig. 3). In that year, the runoff yield was

Fig. 11. Measured and simulated sediment concentrations in 1977 for selected tributaries: (a) Huangfu Station in Huangfuchuan River; (b) Gaoshiya Station in

Gushanchuan River; (c) Wenjiachuan Station in Kuye River; (d) Shenjiawan Station in Jialu River.

10 G. Wang et al. / Journal of Hydro-Environment Research 1 (2007) 1e11

0

2,000

4,000

6,000

8,000

Jul.1 Jul. 11 Jul.21 Jul.31 Aug.10 Aug. 20 Aug. 30Date

Dis

char

ge (m

3 /s)

MeasuredSimulated

0

1,000

2,000

3,000

4,000

5,000

Jul.1 Jul. 11 Jul.21 Jul.31 Aug.10 Aug.20 Aug.30Date

Sedi

men

t dis

char

ge (t

/s) Measured

Simulated

Fig. 12. Flow discharge and sediment load at Longmen station in 1977.

12.09� 109 m3, and the total amount of sediment entering intothe main stream of the Yellow River was 2.39� 109 t. Theyear of 1977 was another typical year that had a large amountof sediment yield and high sediment concentration. However,the annual amount of rainfall was not as large as that in theyear of 1967. Storm rainfalls were concentrated in July andAugust. The two storm rainfall events happened in August ac-counted for 30% of the total amount of the whole year. Be-cause of the concentrated storm rainfalls, the annualsediment yield in the coarse sediment source area in 1977reached the amount of 2.17� 109 t even though the annualrunoff yield was only in a medium level, with a value of8.14� 109 m3.

The values for selected parameters in Table 2 were deter-mined based on the parameters used in Chabagou watershed,with necessary adjustment according to the soil types. The dis-tributions of the runoff depth and erosion modulus, whichcould not be obtained by measured data, could be providedby the DYRIM, such as the results of 1967 (Fig. 10). The cal-culated sediment yield of 1967 was 2.549� 109 t, which isclose to the measured value of 2.39� 109 t. The agreement be-tween the simulated and measured values of sediment yieldwas acceptable.

Simulated sediment concentration processes for the maintributaries of 1977 are shown in Fig. 11. The simulated waterand sediment hydrographs at Longmen station, which is theoutlet of the coarse sediment source area, are shown inFig. 12. Statistics of the sediment load of 8 main tributariesin the Loess Plateau from Huangfuchuan in the north to

Table 3

Sediment load statistics of main tributaries in the year 1977

Tributary Measured

sediment

load (�108 t)

Simulated

sediment

load (�108 t)

Error

percentage (%)

Huangfuchuan 0.26 0.33 26.92

Gushanchuan 0.839 1.21 44.22

Kuye River 1.38 1.52 10.14

Tuwei River 0.211 0.18 �14.69

Jialu River 0.121 0.17 40.5

Sanchuan River 0.465 0.69 48.38

Wuding River 2.69 3.42 27.14

Qingjian River 1.17 0.95 �18.80

Qingjian River in the south are shown in Table 3. The simu-lated sediment runoff had the same order of magnitude asthe field data, and the simulated daily sediment load matchedthe trend of the field processes.

There are two main reasons for the discrepancies be-tween the measured and simulated runoff and sedimentyield values. The first reason is that it is somewhat difficultto calibrate and verify the distributed parameters for sucha large basin. The other one is the rainfall data. Sedimentyield and transport on the Loess Plateau is not only relatedto the quantity of rainfall, but is also influenced by the pro-cess of rainfall intensity. However, the rainfall input adoptedin the simulation was in the format of daily precipitation.Normally a rainfall can’t last for the whole day in this re-gion. Therefore, a day was divided into small time steps,and how many number of time steps that have the rainfallwas determined according to the statistic duration basedon its total amount of precipitation.

6. Concluding remarks

The main erosion processes on the Loess Plateau, includ-ing the water and sediment yield on hillslopes, gravitationalerosion in gully regions, and hyperconcentrated flow routingin channels, were physically formulated. Taking advantageof information technology, these physically-based modelswere integrated as the DYRIM, to provide distributed simu-lation at the river basin scale. Test simulations indicated thatthe model was capable of simulating the distribution of sed-iment yield and transport in a large-scale watershed in theLoess Plateau of the Yellow River. The model can beused to analyze the influence of soil erosion from differentsub-regions and to evaluate the effect of different conserva-tion measures to develop better land use and river manage-ment strategies. Moreover, we have high hopes that theDYRIM may be extended to other basins or become a ge-neric model for soil erosion modeling.

Acknowledgements

This work was supported by the National Natural ScienceFoundation of China (Grant No. 50221903).

11G. Wang et al. / Journal of Hydro-Environment Research 1 (2007) 1e11

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